This paper considers cognitive radio (CR) inspired non-orthogonal multiple-access (NOMA). Such NOMA users with performance improvement can be achieved as deploying relay selection schemes. In this investigation, NOMA and CR scheme are considered as promising techniques to introduce new model of CR-NOMA and to improve spectral efficiency and energy efficiency. In this paper, problem of hardware impairment-aware design is studied to evaluate practical performance as deployment of CR-NOMA in practical. Especially, we examine outage performance of secondary network where contains relay selection strategy under limitation of interference of secondary source and secondary relay on primary destination. The closed-form expressions of outage performance are provided as main metric to exhibit performance analysis. Simulation results show that outage performance is till remained by using NOMA compared to the conventional orthogonal multiple access (OMA). It is also indicated that the performance of Opportunistic Relay Selection (ORS) is better than Partial Relay Selection (PRS) scheme.